A Fast Heuristic Algorithm for the Train Unit Assignment Problem

Authors Valentina Cacchiani, Alberto Caprara, Paolo Toth

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Valentina Cacchiani
Alberto Caprara
Paolo Toth

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Valentina Cacchiani, Alberto Caprara, and Paolo Toth. A Fast Heuristic Algorithm for the Train Unit Assignment Problem. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


In this paper we study a railway optimization problem known as the Train Unit Assignment Problem. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for the best assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. We propose a heuristic algorithm based on the computation of a lower bound obtained by solving an Integer Linear Programming model that gives the optimal solution in a "peak period" of the day. The performance of the heuristic algorithm is computationally evaluated on real-world instances provided by a regional Italian Train Operator. The results are compared with those of existing methods from the literature, showing that the new method is able to obtain solutions of good quality in much shorter computing times.
  • Train Unit Assignment
  • Heuristic Algorithm
  • ILP model
  • Real-world instances


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